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1

The postdoc variant of the secretary problem

Vanderbei Robert J.

Mathematica Applicanda

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2021

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Vol. 49, no. 1

3--13

EN

The classical secretary problem involves sequentially interviewing a pool of n applicants with the aim of hiring exactly the best one in the pool-nothing less is good enough. The optimal decision strategy is easy to describe and the probability of success is 1/e. In this paper, we consider a minor variant of this classical problem. We wish to pick not the best, but the second best (the best is going to Harvard). In this case, an explicit solution can be given both for the optimal strategy and the associated optimal success probability. The probability of success is k*0 (n - k*0) / (n (n - 1)) where k*0 = [n/2]. Clearly, as n goes to infinity, the probability of success tends to 1/4. Apparently, it is easier to pick the best than the second best.

PL

Klasyczny problem sekretarki to sekwencyjne analizowanie n zgłoszeń, wśród których nie ma dwóch identycznych, w celu wyboru najlepszego z kandydatów w chwili, gdy zgłosi się na konkurs- wybór kandydata o innego niż najlepszy nie jest satysfakcjonujący. Optymalna strategia w tym problemie jest łatwa do opisania, a prawdopodobieństwo sukcesu wynosi w przybliżeniu exp(-1). W tym artykule rozważamy wariant tego klasycznego problemu, w którym celem jest wybór dokładnie drugiego co do rangi wśród n kandydatów. Podobnie jak w życiu, na zatrudnienie najlepszego nas nie stać lub piszemy opinie zewnętrzne, i wybieramy dla wybranych najlepsze miejsce na studia doktoranckie. Chcemy wybrać nie najlepszych, ale drugich najlepszych (najlepszy jedzie na Harvard). Również w tym problemie można podać optymalne rozwiązanie: zarówno wskazać optymalną strategię, jak i wyliczyć związane z tą strategią prawdopodobieństwa sukcesu. Szansa na sukces w tym problemie wynosi k*0 (n - k*0) / (n (n - 1), gdzie k0 = [n/2]. Gdy n dąży do nieskończoności, to prawdopodobieństwo sukcesu wynosi ma granicę 1/4. Zatem najwyraźniej łatwiej jest wybrać najlepszego niż drugiego najlepszego.

2

Hidden and Indirect (Probabilistically Estimated) Reputations - Hiper Method

Leszczyński K., Zakrzewicz M.

Foundations of Computing and Decision Sciences

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2015

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Vol. 40, No. 1

35--51

EN

It is a challenge to design a well balanced reputation system for an environment with millions of users. A reputation system must also represent user reputation as a value which is simple and easy to compare and will give users straightforward suggestions who to trust. Since reputation systems rely on feedbacks given by users, it is necessary to collect unbiased feedbacks. In this paper we present a controversial, yet innovative reputation system. Hidden and Indirect (Probabilistically Estimated) Reputations - HIPER Method splits user reputation into two related values: Hidden Reputation (HR) is directly calculated from a set of feedbacks, Indirect Reputation (IR) is a probabilistically estimated projection of the hidden reputation and its value is public. Such indirect connection between received feedbacks and a visible reputation value allows users to provide unbiased feedbacks without fear of retaliation.

3

Mining online auction social networks for reputation and recommendation

Morzy M., Wierzbicki A., Papadopoulos A. N.

Control and Cybernetics

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2009

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Vol. 38, no 1

87-106

EN

Online auctions are quickly becoming one of the leading branches of e-commerce. Unfortunately, online auctions attract many fraudulent activities. Reputation systems are crucial for guaranteeing fairness of trade and reliability of service. Currently used reputation systems offer little protection from malevolent contractors. In this paper we present a new method for mining the reputation of sellers in online auctions. We devise two independent measures that assess reliability and questionability of sellers in parallel, leading to the concept of positive and negative reputation. To compute these measures we construct an S-graph which reflects the social linkage between sellers and buyers. We use both explicit and implicit feedbacks provided by auction participants, carefully identifying missing feedbacks that have been purposefully left out. Based on reputation estimates the community of online auction participants can detect misbehaving contractors and counteract fraud. Thus, the application of social information about reputation of contractors can be perceived as recommendations. Experimental evaluation of our proposal proves the feasibility and usefulness of the presented approach.

4

Wykorzystanie wolnych zasobów w sieciach IP do monitorowania i sygnalizacji stanu sieci

Anszperger B.

Przegląd Telekomunikacyjny + Wiadomości Telekomunikacyjne

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2006

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nr 4

108-113

PL

Sformułowano i opisano koncepcję systemu aukcyjnego, umożliwiającego użytkownikom sieci IP uczestnictwo w procesie definiowania i wyceniania oferowanych im usług. Zaproponowany system składa się z kilku, ściśle ze sobą powiązanych, części nazywanych podsystemami. Jeden z podsystemów wykorzystuje zaproponowaną koncepcję wolnych zasobów sieciowych? jako wygodnego narzędzia monitorowania i sygnalizacji stanu sieci IP, nie wpływając jednocześnie na jakość oferowanych klientowi usług. Następnie zaproponowano prosty protokół wykorzystujący przedstawioną powyżej koncepcję, a także przeprowadzono jego symulację za pomocą własnego modułu symulacyjnego napisanego w języku Perl. W podsumowaniu szeroko omówiono otrzymane wyniki symulacji.

EN

This paper formulates and describes the concept of auctions system, which enables IP network's users to participate in definition of network services, types and prices. Presented system consist of serveral parts, closely realated each other, called subsystems. One of subsystems is utilising proposed lunused network resources concept as efficient way of monitoring and signalling IP networks, state without impacting the quality of services being provided to users. Next, simple protocol supporting proposed concept is presented and simulated with proprietary software module, written in Perl. Simulation's results are presented and broadly discussed.

5

Density-based measure of reputation of sellers in online auctions

Morzy M.

Foundations of Computing and Decision Sciences

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2006

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Vol. 31, No. 1

75-86

EN

Online auctions are gaining tremendous popularity in recent years. Although providing unprecedent opportunities, online auction sites become an attractive environment for fraud. The expansion of the share of online auctions in the world trade causes exponential growth of theft and deception associated with this medium. Participants of online auctions agree that trustworthy reputation systems are an important factor in fighting dishonest and malicious users. Unfortunately, popular auction sites use only very simple reputation estimation schemes that utilize feedbacks issued reciprocally by users after terminated auctions. Such systems can be easily deceived and do not offer sufficient protection against organized fraud. In this paper we present a novel density-based reputation measure. The new reputation measure uses the topology of seller-buyer connections to derive knowledge about trustworthy sellers. We mine the data on past transactions to discover clusters of connected sellers and for each seller we measure the density of the seller's neighborhood. We use these clusters both for scoring the reputation of individual sellers, and to assist buyers in informed decision making by generating automatic recommendations. We perform many experiments on the body of real-world data acquired from a leading Polish provider of online auctions to examine the new measure in detail.